(1) Field of the Invention
The present invention relates to the field of research into the mechanical properties of solid materials. The invention relates more particularly to searching for crack initiation conditions in a part that is to be fabricated and that is to be subjected to fretting-fatigue type stresses. Such fretting-fatigue stresses are known to associate microscopic rubbing on a surface with volume deformation such as in twisting, bending, and/or traction-compression situations.
The present invention lies in the context of a method of fabricating a mechanical part, including a method of making a predictive search concerning the risks of crack initiation in said mechanical part in a fretting-fatigue situation. More specifically, said predictive search makes use of a calculation method of the type implementing finite elements.
(2) Description of Related Art
In the context of a method of fabricating a mechanical part, the structure of the mechanical part is determined before the part is made, in particular by taking account of the ability of that mechanical part to withstand the stresses to which it is to be subjected in operation. In this context, a mechanical part may be placed in a fretting-fatigue situation, and it is appropriate to predict the risk of it cracking, given the characteristics of the material from which it is made. For this purpose, calculation methods of the finite element type have been developed that make it possible to predict the risks of crack initiation in a mechanical part made of a given material.
Defining the structure of a part that is to be fabricated by making use of a finite element type calculation method involves a prior operation of performing tests on test pieces in order to evaluate the strength of the material from which the part is to be fabricated. A search is made more specifically to quantify the thresholds from which cracking is initiated in a given material, and then on the basis of information collected during the tests performed, to calibrate a criterion for application of the finite element calculation method in order to predict the risks of crack initiation in the part that is to be fabricated, depending on its dimensions.
In general terms, the method of calculation by finite elements consists in defining a mesh for a stress contact zone on the part that is to be fabricated, and taking account of the stress gradient in the material from which the part is fabricated. The individual meshes have the shape of regular polygons, in particular triangles or squares, and at their vertices they define nodes for which the applied stresses are calculated. For each of the calculated stresses, a risk of crack initiation is deduced by application of a criterion in the form of a coefficient or an equation. In order to take account of the stress gradient in the material, various calculation techniques may be applied, in particular by taking account of a critical distance in depth.
It is conventional to define a fine mesh based on the smallest possible mesh size and on a specific density of meshes over a surface depth of the material. A fine mesh makes it possible to distribute as well as possible and with accuracy the sizes of the meshes defining the separation distances between adjacent nodes, with the applied stresses being calculated for those nodes along predefined paths. From such a fine mesh, it is desired to obtain results that converge, thereby obtaining an estimate of the risks that is as exact as possible, given the application of a method of calculation involving discretization.
More precisely, it is commonly accepted that the finite element calculation method must be convergent, so that error due to discretization can ideally be considered as being zero, providing the fineness and the density of the mesh tend towards a mesh size of zero. Ideally, the size of the meshes should be considered relative to the grain size of the material from which the part is to be fabricated.
In this context, reference may be made to the following documents:    US 2003/0074976 (Ahmad Jalees);    A. L. Mohd Tobi et al. “A study on the interaction between fretting wear and cyclic plasticity for Ti-6A1-AV”, Wear, Elsevier Sequoia, Lausanne, CH, Vol. 267, No. 1-4, Jun. 15, 2009 (2009 Jun. 15), pp. 270-282; XP026133268, ISSN: 0043-1648, DOI: 10.1016/J.Wear.2008.12.039 (extracted on 2009 May 23); and    S. Naboulsi et al. “Fretting fatigue crack initiation behavior using process volume approach and finite element analysis”, Tribology International, Vol. 36, No. 2, Feb. 2, 2003 (2003-02-02), pp. 121-131, XP055062404, ISSN: 0301-679X, DOI: 10.1016/S0301-679X (02)00139-1.
Searching for a result that converges makes it difficult if not impossible to use such a finite element calculation method on an industrial scale for application to predicting the risks of crack initiation in a part that is to be fabricated. Such an ideal method with converging results requires large amounts of calculation time and prevents the computer equipment that is performing those calculations from being used for any other purpose. Such an approach is particularly unsuitable for a material under examination that withstands steep surface stress gradients, such as an alloy based on titanium or a composite material, e.g. a metal-filled ceramic material. As an indication, in order to obtain results that converge, a fine mesh for a material that is subjected to steep surface stress gradients requires meshes of a size that may be as small 5 micrometers (μm), or indeed meshes of a size that is even smaller, especially for a titanium-based alloy.
For example, in the field of aircraft, and more particularly of rotorcraft, the mechanical parts making up a mechanism are subjected in flight not only to fatigue stresses specific to their own operation, but also to fretting stresses generated by the high levels of vibration that such mechanisms need to withstand. The material from which such mechanical parts are made is selected for its characteristics of being lightweight and robust when faced with stresses applied in volume. Nevertheless, the vibration to which mechanical parts are subjected gives rise to micromovements in the zones of contact between them, thereby giving rise to microscopic surface fretting. It should be considered that the shapes of such mechanical parts may well be complex.
In this context, a material that is suitable for fabricating mechanical parts that are subjected to high levels of fretting-fatigue stress on board an aircraft, and in particular a rotorcraft, is a material based on titanium, such as the titanium alloy Ti-10V-2Fe-3Al, or an analogous material that withstands steep stress gradients, which material is selected because of its light weight and its ability to withstand volume stresses.
It has been found that conventional methods of finite element calculation applied to mechanical parts made of a titanium alloy, and in particular for mechanical parts that are complex in shape, are difficult to use on an industrial scale because of the calculation time needed and because of such parts needing to be designed appropriately to avoid them being overdimensioned.
Such difficulties of making use of conventional finite element calculation methods for defining the structure of a part to be fabricated, in particular one made of a titanium alloy, are mentioned in document US 2003/0074976 (Ahmad Jalees).